Question

If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density $d$ and the distance $r$ from the centre of earth will be

• A. $d\propto r$
• B. $d\propto r^{1/2}$
• C. $d\propto 1/r$
• D. $d\propto \frac{1}{r^2}$

Answer 1

The correct option is C $d\propto 1/r$

$g=\frac{GM}{m^2}$

Now, $m=\frac{4}{3}\pi r^{3}d$ [$d\to$ density]

$\therefore g=\frac{4G\pi r^{3}d}{3r^2}=\frac{4}{3}G\pi rd$

$\Rightarrow d=\frac{3g}{4G\pi r}$

or, $d\propto \frac{1}{R}$